Op Amps for Everyone - The Repeater Builder's Technical ...

Loop Gain Plots are the Key to Understanding Stability
The amplifier gain, A, intercepts the amplitude axis at 20Log(A), and it breaks down at a
slope of –20 dB/decade at ω = ω a . The negative slope continues for all frequencies greater
than the breakpoint, ω = ω a . The closed loop circuit gain intercepts the amplitude axis at
20Log(V OUT /V IN ), and because β does not have any poles or zeros, it is constant until its
projection intersects the amplifier gain at point X. After intersection with the amplifier gain
curve, the closed loop gain follows the amplifier gain because the amplifier is the controlling
factor.
Actually, the closed loop gain starts to roll off earlier, and it is down 3 dB at point X. At point
X the difference between the closed loop gain and the amplifier gain is –3 dB, thus according
to Equation 5–12 the term –20Log(1+Aβ) = –3 dB. The magnitude of 3 dB is √2 , hence
1 (A) 2
2 , and elimination of the radicals shows that Aβ = 1. There is a method
[4] of relating phase shift and stability to the slope of the closed loop gain curves, but only
the Bode method is covered here. An excellent discussion of poles, zeros, and their interaction
is given by M. E Van Valkenberg,[5] and he also includes some excellent prose to
liven the discussion.
5.5 Loop Gain Plots are the Key to Understanding Stability
Stability is determined by the loop gain, and when Aβ = –1 = |1| ∠–180° instability or oscillation
occurs. If the magnitude of the gain exceeds one, it is usually reduced to one by
circuit nonlinearities, so oscillation generally results for situations where the gain magnitude
exceeds one.
Consider oscillator design, which depends on nonlinearities to decrease the gain magnitude;
if the engineer designed for a gain magnitude of one at nominal circuit conditions,
the gain magnitude would fall below one under worst case circuit conditions causing oscillation
to cease. Thus, the prudent engineer designs for a gain magnitude of one under
worst case conditions knowing that the gain magnitude is much more than one under optimistic
conditions. The prudent engineer depends on circuit nonlinearities to reduce the
gain magnitude to the appropriate value, but this same engineer pays a price of poorer
distortion performance. Sometimes a design compromise is reached by putting a nonlinear
component, such as a lamp, in the feedback loop to control the gain without introducing
distortion.
Some high gain control systems always have a gain magnitude greater than one, but they
avoid oscillation by manipulating the phase shift. The amplifier designer who pushes the
amplifier for superior frequency performance has to be careful not to let the loop gain
phase shift accumulate to 180°. Problems with overshoot and ringing pop up before the
loop gain reaches 180° phase shift, thus the amplifier designer must keep a close eye on
loop dynamics. Ringing and overshoot are handled in the next section, so preventing oscillation
is emphasized in this section. Equation 5–14 has the form of many loop gain
transfer functions or circuits, so it is analyzed in detail.
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